where \(\Omega ^{(n,m)}\)  denotes inclusion of \(n^{th}\)  and \(m^{th}\)  order of \(V_0\)  and \(O \equiv D/Q\)  operators in the calculations. In the many-body perturbation theory (MBPT method), the amplitudes of these wave operators can be determined using the generalized Bloch's equation [1]}, [2]}, [3]} for each order of perturbation as given by
\(\begin{aligned}\left[\Omega ^{(n,m)}, H_{DF} \right] P_0 =& Q_0 V_0 \Omega ^{(n-1,m)} P_0 \\&- \sum _{k=1}^{n-1} \Omega ^{(n-k,m)} P_0 V_0 \Omega ^{(k-1,m)} P_0, \\&+Q_0 O \Omega ^{(n,m-1)} P_0 \\&-\sum _{r=1}^{m-1} \Omega ^{(n,m-r)} P_0 O \Omega ^{(n,r-1)} P_0\end{aligned}\) 
